Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #10385 |
396 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^8,47|a^2=d,b^2=dg,c^2=h,e^2=gh,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,i^a=i^46,c^b=cf,e^b=eh,f^b=fg,i^b=i^46,d^c=dg,e^c=egh767 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 72795);